Obviously if you have access to a wind tunnel, MIRA might oblige for instance, you could measure the Drag Coefficient with the ladders on and off, compare the differing CD and use the figures to create either:
A. A carefully sculptured shape, preferably triangular that would disrupt or alter the flow of air over the ladders.
B. Some kind of acoustic or sound wave generator that could produce an exactly opposite out of phase sound to cancel out the whine.
Although this would need to be variable to account for changes in speed, barometric pressure and air density.
C. Go WFP.